1. Field of the Invention
The present invention relates to a process and an apparatus for image magnification, and in particular, to a process and an apparatus for determining values of new pixels which are to be interpolated between original pixel centers constituting an original image.
The process and apparatus for image magnification of the present invention covers both simple image magnifications with a constant pixel density carried out in image display and image printing, and an increase in pixel density, for example, in the conversion from a Group 3 (G4) type to a Group 4 (G4) type in facsimile transmission systems.
2. Description of the Related Art
In the prior art, a high speed projection method for magnifying an image is proposed in Japanese Unexamined Patent Publication A58-97958 and the Journal of the Institute of Image Electronics Engineers of Japan vol. 11, NO. 2, 1982, pp 72.about.pp 83.
The high speed projection method realizes a high speed processing for determination of the concentration of the converted pixels by carrying out a logic calculation instead of an arithmetic calculation, when magnifying an image.
FIG. 1 shows an example of a process in the high speed projection method.
In the high speed projection method, as a first step, a unit area surrounded by four adjacent original pixel centers is divided into four sections each of which corresponds to one of the four adjacent original pixel centers, and all points in each section are nearer to the corresponding one of the four adjacent original pixel centers, than the other three.
As a second step, an area of a converted pixel is projected on the unit area in which the converted pixel center exists as shown in FIG. 1. When magnification rates in the lateral (horizontal) direction and in the longitudinal (vertical) direction are each p and q, a lateral side of the area of the converted pixel is 1/p of a lateral side of an area of an original pixel, and a longitudinal side of the area of the converted pixel is 1/q of a longitudinal side of the area of the original pixel.
When the concentrations of the above four adjacent pixels are each denoted by I.sub.A, I.sub.B, I.sub.C, and I.sub.D, and a proportion of the area of a converted pixel projected on each of the above sections is denoted by W.sub.A, W.sub.B, W.sub.C, and W.sub.D, the concentration of the converted pixel is expressed as I.sub.R =p.SIGMA. I.sub.i *W.sub.i (i=A, B, C, and D), and the calculated value I.sub.R is quantized to a two-valued state. That is, I.sub.R is made to one (black) when the calculated R.sub.R is larger than or equal to 0.5, and R.sub.R is made to zero (white) when the calculated I.sub.R is smaller than 0.5.
In the high speed projection method, the above multiplication and summation for obtaining I.sub.R is replaced by logic calcutions, as explained in the following, to realize a high speed processing.
First, when a center of a converted pixel is within a vicinity of each of the four adjacent original pixel centers, the above calculated value of the concentration I.sub.R is equal to the concentration value of the corresponding (nearest) original pixel regardless of the other three original pixels. The boundary of the vicinity is generally given as a hyperbolic curve for each of the original pixels. However, as the magnification rate becomes large, the boundary comes close to the center of the unit area, i.e., the boundaries for the four original pixels come close to the lines which divide the unit area into the above four sections, i.e., x=0, and y=0. Therefore, a smooth oblique line in an original image becomes a step-like, angular shape when magnified by a large magnification rate.
On the other hand, generally, the hyperbolic boundary causes another calculational complexity. Thus, the boundary lines x.+-.y=.+-.1/2, were assumed in the conventional high speed projection method as shown in FIG. 2, to avoid the step-like, angular shape which appeared in a magnified oblique line, and to reduce the calculational complexity.
Nevertheless, the conventional high speed projection method as mentioned above is effective to realize a smoothness in magnified oblique lines in the angle of 45 degrees only. Hence, the magnified oblique lines with angles other than 45 degrees have an unnatural shape.
FIGS. 3A, 3B, and 3C each show a magnification result of an oblique line image in an original image by the conventional high speed projection method, wherein the angle of the oblique line is 45 degrees in FIG. 3A, a middle angle between 45 degrees and 90 degrees in FIG. 3B, and a middle angle between 0 and 45 degrees in FIG. 3C, respectively.
As shown in FIGS. 3A, 3B, and 3C, a satisfactorily smooth magnification is not assurerd for oblique lines in an angle other than 45 degree. In particular, when a magnification rate becomes large, the step-like shape becomes prominent.